Earth's diffuse aurora occurs over a broad latitude range and is primarily caused by the precipitation of low-energy (0.1-30-keV) electrons originating in the central plasma sheet, which is the source region for hot electrons in the nightside outer magnetosphere. Although generally not visible, the diffuse auroral precipitation provides the main source of energy for the high-latitude nightside upper atmosphere, leading to enhanced ionization and chemical changes. Previous theoretical studies have indicated that two distinct classes of magnetospheric plasma wave, electrostatic electron cyclotron harmonic waves and whistler-mode chorus waves, could be responsible for the electron scattering that leads to diffuse auroral precipitation, but it has hitherto not been possible to determine which is the more important. Here we report an analysis of satellite wave data and Fokker-Planck diffusion calculations which reveals that scattering by chorus is the dominant cause of the most intense diffuse auroral precipitation. This resolves a long-standing controversy. Furthermore, scattering by chorus can remove most electrons as they drift around Earth's magnetosphere, leading to the development of observed pancake distributions, and can account for the global morphology of the diffuse aurora.